264 On the Use of Definitiojis, an agreement upon the subject discussed, seems, so far as experience shews, to be far from certain. It is however a question much too wide for these pages. But it may not be unsuitable to this place to treat the matter in a more philological manner, and to shew by some instances how the adoption of exact definitions, and the consequent introduction of fixed technical terms, appears to have been connected with the progress of real and certain knowledge in those branches of human speculation which are now considered to be past all danger from controversy. It will be found, it is conceived, that in these cases exact definitions have been, not the causes, but the conse- quences of an advance in our knowledge : that terms have been vague and ambiguous and ill-defined, so long as men's perception of the laws of facts was obscure and incomplete: that new discoveries, even while imperfect and confused, in- troduced new terms, not admitting probably of strict defini- tion, but yet not without their use : that when the laws so discovered became clear and entire, the requisite terms were easily and immediately provided with a greater exactness of meaning. In these, the progressive sciences, the case has been that the real logomachies have taken place among those who attached much importance to definitions ; who, having nothing to add to human knowledge, wished to alter the mode of presenting that which was already known. Persons thus ready to wrangle about the meaning of words have been found at every stage of the progress of truth ; but truth has generally passed rapidly forwards, and left them behind to enjoy their favourite amusement. We shall take a few instances of scientific terms and their definitions, beginning with the most exact and complete sciences. Pure mathematics (Geometry and Analysis) can hardly supply us with a case in point; for in such speculations there can be, properly speaking, no new truth; none, that is, which was not necessarily involved in what we knew before. In the provinces of physical philosophy, definitions are needed to express the principles from which our reasonings must proceed; but in pure mathematics the definitions are themselves the first principles of our reasonings ; and if these
